Question

(1 point) A scientist is measuring the random motions of 500 small particles in water at 20∘∘C, in a long, very thin tube. She places all of the particles in a very small point in the middle of the horizontal tube and 60 seconds later, with the aid of a magical camera, she records all of their positions relative to the point of insertion. Arbitrarily, particles to the left of the insertion point are registered as "negative" and those to the right are "positive". She obtains the following table that records the number of particles observed at every approximate displacement.

Numbers of particles found at various displacements from the insertion point

Number	Approximate Displacement, x (?μm)
2	-400
5	-300
33	-200
118	-100
190	0
107	100
35	200
9	300
1	400

(a) Determine the mean displacement. (Think: does this agree with what you would expect? Relatively speaking, how far off is it?)

Mean displacement = ? ?μm

(b) Determine the root mean square displacement.

Root mean square displacement = ? ?μm

(c) Determine the diffusion coefficient (note the dimensionality of this problem).

D = ? m22/s

Diffusion coefficients and masses of various substances

Substance	Diffusion Coefficient, D (m22/s) in water at 20∘∘C	M (kg/mol)
Water (H22O)	2.00×10−92.00×10−9	0.018
Sucrose	4.59×10−104.59×10−10	0.342
Lysozyme	1.19×10−101.19×10−10	14.1
Bovine serum albumin (BSA)	6.1×10−116.1×10−11	66.5
Fibrinogen (human)	1.98×10−111.98×10−11	330
Bushy stunt virus	1.15×10−111.15×10−11	1.07×1041.07×104
Tobacco mosaic virus	4.4×10−124.4×10−12	4.0×1044.0×104

(d) What particles might these be? (see the table above for diffusion coefficients)
A. Lysozyme
B. Bushy Stunt Virus
C. Fibrinogen (Human)
D. Water

(e) Use the Stokes-Einstein equation to estimate the diameter of these quasi-spherical particles. (You may need to consult table 12.1)

Diameter = ? m

Answer 1